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多元分布的 Zonoid 修剪AI 解读

A family of trimmed regions is introduced for a probability distribution in Euclidean d-space. The regions decrease with their parameter $\alpha$, from the closed convex hull of support (at $\alpha = 0$) to the expectation vector (at $\alpha = 1$). The family determines the underlying distribution uniquely. For every $\alpha$ the region is affine equivariant and continuous with respect to weak convergence of distributions. The behavior under mixture and dilation is studied.…

多元分布的洛伦兹 zonoidAI 解读

The article extends the usual Lorenz curve and Lorenz order of univariate distributions to the multivariate case. For a given probability distribution in nonnegative d space, d ≥ 1, we define and investigate the Lorenz zonoid and the Lorenz surface, which are sets in (d + 1) space. The surface equals the usual Lorenz curve when d = 1. Included is the definition of the Lorenz surface of a finite number of vectors that may be interpreted as the endowments of economic units in…